Sentence examples for solutions to the initial from inspiring English sources

The uniqueness proof for solutions to the initial value problem for Einstein's field equations contains an "up to diffeomorphism" proviso.

Finally, we consider nonexistence of weak solutions to the initial problem (1.3).

Then, we prove that the discrete solutions of the relaxed problem are the solutions to the initial problem.

Liu and Zhou also gave the classical solutions to the initial boundary problem of time-like extremal surface [5, 6].

Sun and Zhang [20] obtained the existence of global strong solutions to the initial boundary value problem.

The purpose of this section is to prove global existence and optimal decay estimate of solutions to the initial value problem (1.1), (1.2).

Wang [22] established large solutions to the initial-boundary value problem for planar magnetohydrodynamics.

The existence and uniqueness of local-in-time solutions to the initial-boundary value problem (1.2) is well known [15].

Secondly, we will study the stability of weak solutions to the initial-boundary value problem (1.4 - 1.2 - 1.7).

We study the local and global existence and asymptotic behavior for solutions to the initial-boundary value problem: (1.1).

Wang [18] established the existence of large solutions to the initial-boundary value problem for planar magnetohydrodynamics.